def test_precond_LinearLeastSquares(self):
n = 5
_A = np.eye(n) + 0.01 * util.randn([n, n])
A = linop.MatMul([n, 1], _A)
x = util.randn([n, 1])
y = A(x)
x_lstsq = np.linalg.lstsq(_A, y, rcond=-1)[0]
p = 1 / (np.sum(abs(_A)**2, axis=0).reshape([n, 1]))
P = linop.Multiply([n, 1], p)
x_rec = app.LinearLeastSquares(A, y, show_pbar=False).run()
npt.assert_allclose(x_rec, x_lstsq, atol=1e-3)
alpha = 1 / app.MaxEig(P * A.H * A, show_pbar=False).run()
x_rec = app.LinearLeastSquares(A,
y,
solver='GradientMethod',
alpha=alpha,
max_power_iter=100,
max_iter=1000,
show_pbar=False).run()
npt.assert_allclose(x_rec, x_lstsq, atol=1e-3)
tau = p
x_rec = app.LinearLeastSquares(A,
y,
solver='PrimalDualHybridGradient',
max_iter=1000,
tau=tau,
show_pbar=False).run()
npt.assert_allclose(x_rec, x_lstsq, atol=1e-3)
def test_LinearLeastSquares(self):
n = 5
_A = np.eye(n) + 0.1 * np.ones([n, n])
A = linop.MatMul([n, 1], _A)
x = np.arange(n).reshape([n, 1])
y = A(x)
z = np.arange(n).reshape([n, 1])
for mu in [0, 0.1]:
for lamda in [0, 0.1]:
for proxg in [None, prox.L2Reg([n, 1], lamda)]:
for alg_name in [
'GradientMethod', 'PrimalDualHybridGradient',
'ConjugateGradient'
]:
with self.subTest(proxg=proxg,
alg_name=alg_name,
lamda=lamda,
mu=mu):
if proxg is None:
prox_lamda = 0
else:
prox_lamda = lamda
x_numpy = np.linalg.solve(
_A.T @ _A +
(lamda + mu + prox_lamda) * np.eye(n),
_A.T @ y + mu * z)
if (alg_name == 'ConjugateGradient'
and proxg is not None):
with self.assertRaises(ValueError):
app.LinearLeastSquares(
A,
y,
alg_name=alg_name,
lamda=lamda,
proxg=proxg,
mu=mu,
z=z,
show_pbar=False).run()
else:
x_rec = app.LinearLeastSquares(
A,
y,
alg_name=alg_name,
lamda=lamda,
proxg=proxg,
mu=mu,
z=z,
show_pbar=False).run()
npt.assert_allclose(x_rec, x_numpy, atol=1e-3)
def test_LinearLeastSquares(self):
n = 5
_A = np.eye(n) + 0.1 * np.ones([n, n])
A = linop.MatMul([n, 1], _A)
x = np.arange(n).reshape([n, 1])
y = A(x)
for z in [None, x.copy()]:
for lamda in [0, 0.1]:
for proxg in [None, prox.L2Reg([n, 1], lamda)]:
for solver in [
'GradientMethod', 'PrimalDualHybridGradient',
'ConjugateGradient', 'ADMM'
]:
with self.subTest(proxg=proxg,
solver=solver,
lamda=lamda,
z=z):
AHA = _A.T @ _A + lamda * np.eye(n)
AHy = _A.T @ y
if proxg is not None:
AHA += lamda * np.eye(n)
if z is not None:
AHy = _A.T @ y + lamda * z
x_numpy = np.linalg.solve(AHA, AHy)
if (solver == 'ConjugateGradient'
and proxg is not None):
with self.assertRaises(ValueError):
app.LinearLeastSquares(
A,
y,
solver=solver,
lamda=lamda,
proxg=proxg,
z=z,
show_pbar=False).run()
else:
x_rec = app.LinearLeastSquares(
A,
y,
solver=solver,
lamda=lamda,
proxg=proxg,
z=z,
show_pbar=False).run()
npt.assert_allclose(x_rec, x_numpy, atol=1e-3)
def test_proxg_LinearLeastSquares(self):
n = 5
mat = np.eye(n) + 0.1 * util.randn([n, n])
A = linop.MatMul([n, 1], mat)
x = util.randn([n, 1])
y = A(x)
lamda = 0.1
x_lstsq = np.linalg.solve(np.matmul(mat.conjugate().T, mat) + lamda * np.eye(n),
np.matmul(mat.conjugate().T, y))
proxg = prox.L2Reg([n, 1], lamda)
x_rec = app.LinearLeastSquares(
A, y, alg_name='GradientMethod', max_iter=1000, proxg=proxg).run()
npt.assert_allclose(x_rec, x_lstsq)
x_rec = app.LinearLeastSquares(A, y, max_iter=1000, proxg=proxg,
alg_name='PrimalDualHybridGradient').run()
npt.assert_allclose(x_rec, x_lstsq)
def test_LinearLeastSquares(self):
n = 5
mat = np.eye(n) + 0.1 * util.randn([n, n])
A = linop.MatMul([n, 1], mat)
x = util.randn([n, 1])
y = A(x)
x_lstsq = np.linalg.lstsq(mat, y, rcond=-1)[0]
x_rec = app.LinearLeastSquares(A, y).run()
npt.assert_allclose(x_rec, x_lstsq)
x_rec = app.LinearLeastSquares(
A, y, alg_name='GradientMethod', max_iter=1000).run()
npt.assert_allclose(x_rec, x_lstsq)
x_rec = app.LinearLeastSquares(A, y, max_iter=1000,
alg_name='PrimalDualHybridGradient').run()
npt.assert_allclose(x_rec, x_lstsq)
def test_dual_precond_LinearLeastSquares(self):
n = 5
mat = np.eye(n) + 0.1 * util.randn([n, n])
A = linop.MatMul([n, 1], mat)
x = util.randn([n, 1])
y = A(x)
x_lstsq = np.linalg.lstsq(mat, y, rcond=-1)[0]
d = 1 / np.sum(abs(mat)**2, axis=1, keepdims=True).reshape([n, 1])
x_rec = app.LinearLeastSquares(A, y, alg_name='PrimalDualHybridGradient',
max_iter=1000, sigma=d).run()
npt.assert_allclose(x_rec, x_lstsq)
def test_l2reg_bias_LinearLeastSquares(self):
n = 5
mat = np.eye(n) + 0.1 * util.randn([n, n])
A = linop.MatMul([n, 1], mat)
x = util.randn([n, 1])
y = A(x)
z = util.randn([n, 1])
lamda = 0.1
mu = 0.01
x_lstsq = np.linalg.solve(np.matmul(mat.conjugate().T, mat) + (lamda + mu) * np.eye(n),
np.matmul(mat.conjugate().T, y) + mu * z)
x_rec = app.LinearLeastSquares(A, y, lamda=lamda, mu=mu, z=z).run()
npt.assert_allclose(x_rec, x_lstsq)
x_rec = app.LinearLeastSquares(
A, y, alg_name='GradientMethod', max_iter=1000, lamda=lamda, mu=mu, z=z).run()
npt.assert_allclose(x_rec, x_lstsq)
x_rec = app.LinearLeastSquares(A, y, max_iter=1000, lamda=lamda, mu=mu, z=z,
alg_name='PrimalDualHybridGradient').run()
npt.assert_allclose(x_rec, x_lstsq)
def test_precond_LinearLeastSquares(self):
n = 5
mat = np.eye(n) + 0.1 * util.randn([n, n])
A = linop.MatMul([n, 1], mat)
x = util.randn([n, 1])
y = A(x)
x_lstsq = np.linalg.lstsq(mat, y, rcond=-1)[0]
p = 1 / (np.sum(abs(mat)**2, axis=0).reshape([n, 1]))
P = linop.Multiply([n, 1], p)
x_rec = app.LinearLeastSquares(A, y).run()
npt.assert_allclose(x_rec, x_lstsq)
alpha = p / app.MaxEig(P * A.H * A).run()
x_rec = app.LinearLeastSquares(A, y, alg_name='GradientMethod',
max_iter=1000, alpha=alpha).run()
npt.assert_allclose(x_rec, x_lstsq)
tau = p
x_rec = app.LinearLeastSquares(A, y, alg_name='PrimalDualHybridGradient',
max_iter=1000, tau=tau).run()
npt.assert_allclose(x_rec, x_lstsq)
def test_dual_precond_LinearLeastSquares(self):
n = 5
_A = np.eye(n) + 0.1 * util.randn([n, n])
A = linop.MatMul([n, 1], _A)
x = util.randn([n, 1])
y = A(x)
x_lstsq = np.linalg.lstsq(_A, y, rcond=-1)[0]
d = 1 / np.sum(abs(_A)**2, axis=1, keepdims=True).reshape([n, 1])
x_rec = app.LinearLeastSquares(A,
y,
solver='PrimalDualHybridGradient',
max_iter=1000,
sigma=d,
show_pbar=False).run()
npt.assert_allclose(x_rec, x_lstsq, atol=1e-3)